Dilemma of Dilemmas: How Collective and Individual Perspectives Can Clarify the Size Dilemma in Voluntary Linear Public Goods Dilemmas

Abstract

Empirical findings on public goods dilemmas indicate an unresolved dilemma: that increasing size—the number of people in the dilemma—sometimes increases, decreases, or does not influence cooperation. We clarify this dilemma by first classifying public goods dilemma properties that specify individual outcomes as individual properties (e.g., Marginal Per Capita Return) and group outcomes as group properties (e.g., public good multiplier), mathematically showing how only one set of properties can remain constant as the dilemma size increases. Underpinning decision-making regarding individual and group properties, we propose that individuals are motivated by both individual and group preferences based on a theory of collective rationality. We use Van Lange's integrated model of social value orientations to operationalize these preferences as an amalgamation of outcomes for self, outcomes for others, and equality of outcomes. Based on this model, we then predict how the public good's benefit and size, combined with controlling individual versus group properties, produce different levels of cooperation in public goods dilemmas. A two (low vs. high benefit) by three (2-person baseline vs. 5-person holding constant individual properties vs. 5-person holding constant group properties) factorial experiment (group n = 99; participant n = 390) confirms our hypotheses. The results indicate that when holding constant group properties, size decreases cooperation. Yet when holding constant individual properties, size increases cooperation when benefit is low and does not affect cooperation when benefit is high. Using agent-based simulations of individual and group preferences vis-à-vis the integrative model, we fit a weighted simulation model to the empirical data. This fitted model is sufficient to reproduce the empirical results, but only when both individual (self-interest) and group (other-interest and equality) preference are included. Our research contributes to understanding how people's motivations and behaviors within public goods dilemmas interact with the properties of the dilemma to lead to collective outcomes.

Cooperation in Groups of Different Sizes: The Effects of Punishment and Reputation-Based Partner Choice

“…Partially supporting Hypothesis 1a, when temptation increased with group size, 20-person groups cooperated significantly less than 4-person groups, yet surprisingly, 40-person and 4-person groups did not vary in cooperation. Unexpectedly, inconsistent with previous research (Barcelo and Capraro, 2015;Shank et al, 2015), we found no statistical difference in cooperation across groups of 4, 20, and 40 when gain increased with group size (i.e., fixed MPCR). Thus, keeping the MPCR fixed may buffer against potential negative consequences of larger groups for cooperation and collective action.…”

“…Specifically, when the group payoff (MGR) is fixed, gain remains constant but temptation increases with group size, such that the personal benefit from cooperation decreases in larger groups. In contrast, when the individual payoff (MPCR) is fixed, larger groups produce greater added benefits when all cooperate (vs. no one cooperates), such that temptation remains constant but gain increases with group size, making cooperation more likely to occur in larger groups (see Isaac et al, 1994;Barcelo and Capraro, 2015;Shank et al, 2015). Thus, people may adjust their cooperation level depending on how temptation and gain shift as a function of the size of the interacting group.…”

Culture and cooperation in a spatial public goods game

“…Another potentially important factor in the public goods game is the group size [60,[66][67][68][69][70][71][72][73]. Some properties, such as the pool multiplier m, are properties of the group, and some, such as the marginal per capita return (MPCR), relate to the individual.…”

“…The MPCR (which we will denote β) is defined as β = m N where N is the group size. Therefore either m or MPCR can be held constant when the group size changes, but not both [73].…”

“…eliminating the group size as a factor. In this way, the individual property MPCR is held constant as the group size varies so that the payoff does not depend directly on group size [73]. The total payoff for agent i over all the games is B i = j B ij .…”